Ind. Eng. Chem. Res. 1996,34,1320-1326
1320
GENERAL RESEARCH Chemical Equilibria in the Process of Etherification of Light FCC Gasoline with Methanol Andrzej Wyczesany Institute of Organic Chemistry and Technology, University of Technology, 31-155 Krakbw, Poland
The paper presents the thermodynamic analysis of the process of etherification of light FCC gasoline with methanol. In the model presented, it is assumed that the chemical equilibria are reached only for the reactions of methanol with C4-C7 olefins having the double bond on a tertiary carbon atom and the reactions of isomerization of olefins and ethers do not take place. Thermodynamic data which were not available from tables (the Gibbs free energies of formation of C7 olefins and c6-C~ethers) were calculated using two essentially different group contribution methods (the Benson method and the Yoneda method) to investigate the influence of the data obtained this way on the calculated equilibrium compositions. The nonideality of the liquid phase was described by the modified UNIFAC method and by the ASOG method. In both cases very similar equilibrium compositions were obtained. The parameters were specified for which the system begins to be in the simultaneous chemical and phase (vapor-liquid) equilibrium.
Introduction
Thermodynamic Model
Future gasoline will have restricted amounts of aromatics, particularly benzene. Therefore, ethers with high octane numbers and relatively low vapor pressure, which can additionally decrease CO and ozone emissions in the combustion gases, are becoming increasingly interesting. Besides methyl tert-butyl ether (MTBE) already in commercial use, c6-c8 ethers originating from (2547 olefins begin to attract attention. Pilot plant results show that light FCC gasoline etherification proceeds with a quite profitable yield (Pescarollo et al.,
A useful tool to calculate the equilibrium compositions of multicomponent systems is the BNR algorithm of Smith and Missen (1982).It is based on the minimization of the Gibbs free energy of the entire mixture subject to side conditions of elemental abundances and nonnegativity of the mole numbers: N
g = Cnyi = (min)
(1)
i=l
1993). The objective of this paper is the evaluation of thermodynamic limits of the process considered in which a very large number of components is involved. Such a kind of investigation has not yet been carried out. According to experimental results (Pescarollo et al., 19931,only olefins with double bond on a tertiary carbon atom (referred to as reactive olefins in the following) exhibit a tendency to react with methanol. The amount of the other hydrocarbons contained in gasoline (paraffins, cycloparaffins, aromatics, and the remaining olefins) is nearly the same in the feed and in the reaction products, which implies that the remaining olefins do not isomerize to reactive ones. Therefore, it was assumed that the chemical equilibrium is reached by reactions of reactive olefins with methanol only and that the resulting ethers as well as the hydrocarbons contained in the feed do not isomerize. Thus, the system reaches the so-called restricted chemical equilibrium. One of the difficulties which had to be overcome working on the problem considered is the shortage of some thermodynamic data (especially the standard Gibbs free energies of formation) of C7 olefins and c6c8 ethers. These data were calculated by the group contribution methods using two essentially different approaches (the Benson method and the Yoneda method, both described in Reid et al., 1987) to investigate the effect of the procedure applied on the final equilibrium composition. 0888-588519512634-1320$09.00/0
niI0
i = 1, 2,..., N
(3)
where g is the Gibbs free energy of the entire mixture, n, the number of moles of species i, p, the chemical potential of species i, Uki the number of atoms of element FZ in species z, bk the moles of element K in feed, N the number of species, and M the number of elements. The original computational program written on the basis of the BNR algorithm can be applied to ideal systems only. In this paper the developed version of that program was used (Wyczesany,1993). This version can be applied to the calculation of simultaneous chemical and phase equilibria, in multicomponent and multiphase systems. The program developed uses expressions describing the chemical potential of real components in an explicit form. For the gas phase this expression is always given in the general form
where P is the total pressure, poi the standard chemical potential of species i referred to the ideal gas state, nT the total number of moles including inerts, and @i the 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1321 Table 1. List of the Reactions
- MTBE -
Cd Class
+ methanol
isobutene
C5 Class
3 3
2-methyl-2-butene 2-methyl-l-butene
+ methanol
2-methyl-l-pentene 2-methyl-2-pentene cis-3-methyl-2-pentene
+ methanol 2-methyl-2-methoxypentane + methanol - 3-methyl-3-methoxypentane
2-methyl-2-methoxybutane
CSClass
1
truns-3-methyl-2-pentene 2-ethyl-l-butene 2,3-dimethyl-l-butene 2,3-dimethyl-2-butene} l-methylcyclopentene
+ methanol - 2,3-dimethyl-2-metoxybutane + methanol - l-methyl-l-methoxycyclopentane C7 Class
3
2-methyll-hexene 2-methyl-2-hexene cis-3-methyl-2-hexene truns-3-methyl-2-hexene cis-3-methyl-3-hexene trans-3-methyl-3-hexene 2-ethyl-l-pentene 2,3-dimethyl-l-pentene 2,3-dimethyl-2-pentene}
I
+ methanol - 2-methyl-2-methoxyhexane + methanol - 3-methyl-3-methoxyhexane
+ methanol - 2,3-dimethyl-2-methoxypentane + - 2,3-dimethyl-3-methoxypentane + methanol - 2,4-dimethyl-2-methoxypentane + methanol - 3-ethyl-3-methoxypentane + methanol - 2,3,3-trimethyl-2-methoxybutane + methanol - l-ethyl-l-methoxycyclopentane
cis-3,4-dimethyl-2-pentene truns-3,4-dimethyl-2-pentene methanol 2-ethyl-3-methyl-l-butene
1
2,4-dimethyl-l-pentene 2,4-dimethyl-2-pentene 3-ethyl-2-pentene
2,3,3-trimethyl-l-butene l-ethylcyclopentene 1,2-dimethylcyclopentene 1,5-dimethylcyclopentene
3 3
1,3-dimethylcyclopentene 1,4-dimethylcyclopentene l-methylcyclohexene
+ methanol - 1,2-dimethyl-l-methoxycyclopentane + methanol - 1,3-dimethyl-l-methoxycyclopentane + methanol - l-methyl-l-methoxycyclohexane
fugacity coefficient of species i to be determined from the adequate EOS. For the problem considered the expression describing the chemical potential in the liquid phase is based on the activity coefficient approach and has the folIowing form:
where p i is the saturated vapor pressure of pure component i, the fugacity coefficient of saturated vapor of pure component i at T and p i , the liquid molar volume of pure component i, and yi the activity coefficient of component i calculated using the modified UNIFAC method. The feed of the process is methanol and light FCC gasoline (35- 100 "C) after a selective hydrogenation of diolefins. According to the above-mentioned assumptions all components of the gasoline with the exception of C4-C7 reactive olefins are treated as inerts. The reactive olefins form 1,4, and 11Of c6,C7, and CSethers, due to the reactions listed in Table 1. According to the assumption about the absence of the isomerization reactions the individual ethers are formed &om the corresponding olefins only (for example, 2-methyl-2-methoxypentane from 2-methyl-l-pentene and 2-methyl-2-pentene). Therefore, it was necessary to distinguish individual groups of components by adding one fictitious element X, to the corresponding reactants and products. Thus, 2-methyl-l-butene, 2-methyl-2butene, and 2-methyl-2-methoxybutane can be described by formulas as C~HIO(XI)I, C~H~O(XI)I, and C6H1401(Xl)l,
and 2-methyl-l-pentene,2-methyl-2-pentene,and 2-methyl-2-methoxypentane as CSHI~(X~)I, C6H12(&)1, and C7H1601(X2)1, and so on. The number of the fictitious elements introduced this way was equal t o 16. This procedure precluded formally, for example, reactions between c6 and C7 olefins or between 2-methyl-2pentene and cis-3-methyl-2-pentene but permitted the reactions of methanol with every reactive olefin. The bk values (eq 2) of the individual fictitious elements X, were equal to the total mole numbers of the olefins contained in the feed and marked by the X, element. The method used is equivalent to the approach described by Smith and Missen (1982) where any additional constraints of the form Dn = d may be incorporated into the formula matrix A' and elementabundance vector b' by means of
A' =
(b)
b' =
(i)
Thus, all the constraints are expressed in the single equation A n = b'. The next problem to be taken into consideration was the presence of inert components in the feed. These compounds do not react, but they affect the total equilibrium composition by the activity coefficients and/ or the fugacity coefficients. It was assumed that the inerts contained in the light FCC gasoline were represented by selected hydrocarbons: paraffins by n-butane, n-pentane, 2-methylbutane, n-hexane, 2,2-dimethylbutane, n-heptane, and 2,2,34rimethylbutane; inert olefins by l-butene, l-pentene, 3-methyl-l-butene, l-hexene, 3,3-dimethyl-l-butene,and l-heptene; cycloparaffins by cyclopentane, cyclohexane, and methylcyclohexane; and aromatics by benzene. In the case of the two-phase
1322 Ind. Eng. Chem. Res., Vol. 34,No. 4, 1995 Table 2. Number of Species in the Gasoline reactive inert olefins olefins paraffins cycloparaffins c4 c5 c6
c7
1 2 8 22
1 2 2 1
1 2 2 2
Table 3. Gasoline Composition feed isobutene C4 inert olefins Cq paraffins C5 reactive olefins CSinert olefins C5 paraffins C5 cycloparaffins c6 reactive olefins c6 inert olefins c6 paraffins c6 cycloparaffins c6 aromatics C7 reactive olefins C7 inert olefins C7 paraffins C7 cycloparaffins total
aromatics
1 1 1
1
wt%
0.57 0.47 0.50 10.39 9.00 19.00 1.oo 10.22 8.80 17.00 1.00 3.00 4.91 4.64 9.00 0.50 100.00
reacting systems the equilibrium mole numbers of the individual inert species in each phase are the result of the phase equilibrium. Therefore, the inert species must be treated as the reacting components (it is not necessary for the one-phase systems). In the model under discussion every inert hydrocarbon was regarded as a species consisting of one atom of a fictitious element (different for every hydrocarbon). The bk values (eq 2) for the individual inert hydrocarbons were equal to the amount of their mole numbers in the feed but did not affect the C and H elemental abundances of the system. Thus, the two-phase system under discussion consisted of 136 species (methanol, 33 reactive olefins, 17 ethers, and 17 inert hydrocarbons in each phase) and 35 elements (C, H, 16 fictitious elements to mark the individual groups of olefins and ethers and 17 fictitious elements standing for inert hydrocarbons). The onephase system consisted of 68 species and 18 elements. Number of species in the gasoline is presented in Table 2. Table 3 presents the gasoline composition in respect of individual classes and groups of hydrocarbons estimated on the basis of the figures and Table 3 of the paper by Pescarollo et al.(1993). The more detailed feed composition required for the equilibrium calculations and presented in Table SI11 (Tables SI-SIV are supplementary material; see paragraph at end of paper regarding availability of supplementary material) was established arbitrarily.
Thermodynamic Data The following values have an influence on the calculated equilibrium composition: the standard chemical potentials poi (identified with the standard Gibbs free energies of formation), the saturated vapor pressures of pure components, pi",and the coefficients q$, #, and yi describing the nonideality of the system. The fourth expression in eq 5 was omitted, because of its negligible effect on the final results. The thermodynamic tables present poi values for C4c6 olefins, methanol, and MTBE (Stull et al., 1969).The values of the standard chemical potentials of C7 reactive olefins and c6-c8 ethers had to be calculated by group
contribution methods. Since these methods give approximate values of p",, these values were calculated using the Benson method (Reid et al., 1987) and by the essentially different Yoneda method (Reid et al., 1987) to estimate the influence of the method applied on the calculated equilibrium composition. (In the case of the Benson method the p", values for the C7 chain olefins were taken from Alberty and Gehrig, 1985). The computational program uses as the input data the temperature function of poi of the following form: poi = A,
+ A,T + A,?a + A 3 p + A4TIn T
(6)
Table SI presents the coefficients Ao-A4 of the components for which both group contribution methods were applied. These coefficients were estimated by the least-squares method from the pol values calculated before for several temperatures in the range 298-1000 K. The vapor pressure values were taken from Reid et al. (1987) and Zwolinski and Wilhoit (1971) for methanol, MTBE, c4-c6 reactive olefins, C7 chain reactive olefins, methylcyclohexene, and all inert hydrocarbons considered. For five C7 reactive cycloolefins and (26c8 ethers pr values were calculated by the Riedel method (Reid et al., 1987). This method permits the calculation of the saturated vapor pressures of a compound from the normal boiling point (TB) and critical parameters (T,and Pc). The TBvalues were taken from Pescarollo et al. (1993) for five C7 cycloolefins and calculated by the group contribution method presented by Reid et al. (1987) for c6-c8 ethers. The critical parameters are necessary also for calculation of $i and 4: coefficients (when the UNIFAC method is applied). The numerical values of T,and P, were taken from Reid et al. (1987). However, for some C7 reactive olefins and c6-cS ethers they had to be calculated by group contribution methods (the Joback method for olefins and the Ambrose method for ethers, as published in Reid et al., 1987). The differences between literature and calculated data for some compounds are presented in Table SII. These examples show that the group contribution methods yield good estimations of calculated values of olefins and ethers. Preliminary calculations exhibited that using literature data the equilibrium conversion of isobutene in the reaction of 1 mol of C4H8 with 1 mol of methanol was equal t o 97.1% (at T = 355 K and P = 13 bar). This value was equal to 98.2%for the same parameters when the data ( p o l ,TB, pQ,T,,P,)for isobutene and MTBE were calculated by the group contribution methods. So the difference was very small.
Results and Discussion The results of the calculations of the equilibrium compositions at T = 355 K and P = 5 bar (product in the liquid phase) for 100 mol of gasoline and 30 mol of methanol (with a weight ratio of gasoline to methanol close to 100:12) are presented in Table SIII. The results are given for the data obtained by two different group contribution methods. It can be seen that conversions of individual c4-c6 reactive olefins are similar for both methods (with the exception of l-methylcyclopentene). As a result of this the differences in the overall conversions of the individual groups of Cgc6 reactive olefins do not exceed 3.1% for both methods. More significant differences appear in the case of some
Ind. Eng. Chem. Res., Vol. 34,No. 4,1995 1323 Table 4. Influence of Temperature on the Calculated Equilibrium Composition (in wt %ha Comparison with the Results of the Pilot Plant6 temp, K compound isobutene C5 reactive olefins c.5 reactive olefins C7 reactive olefins conjugated diolefins inert hydrocarbons dimethyl ether MTBE CS ethers C7 ethers C8 ethers other formed total methanol isobutene conversion, % C5 react olef conv, % c.5react olef conv, % C7 react olef conv, %
340
355
370
385
400
0.002 0.761 1.278 1.529
0.003 1.161 1.786 1.829
0.006 1.680 2.371 2.137
0.010 2.321 3.013 2.448
0.016 3.070 3.696 2.755
73.914
73.914
73.914
73.914
73.914
0.888 14.027 12.323 4.473
0.886 13.445 11.621 4.076
0.882 12.688 10.814 3.667
0.875 11.754 9.926 3.254
0.865 10.663
0.09 3.24 5.84 3.77 0.04 74.09 0.05 0.51 12.71
2.846
5.19
106.809
0.15 105.70
5.144 97.2 70.5 63.8 43.9
6.32 84.2 68.8 42.9 23.2
109.195 2.758 99.7 92.7 87.5 68.9
108.720 3.233 99.5 88.8 82.5 62.8
108.158 3.796 99.0 83.8 76.8 56.5
107.515 4.438 98.3 77.7 70.5 50.1
pilot plant results
a P = 12 bar; the feed composition for the calculations is the same as that in Table SIII. Results of the pilot plant were taken from Pescarollo et al. (1993).
C7 olefins (especially cyclic olefins) which has an influence on the divergence in conversion of the entire group of C7 reactive olefins (10% for both methods). This phenomenon can be explained by the fact that poi of C7 olefins as well as of Cg ethers were calculated by the group contribution methods, whereas poi of c4-c6 olefins and MTBE were taken from the thermodynamic tables. On the other hand, it should be emphasized that C7 reactive olefins are present in much less amounts in the gasoline 35-100 "C than c5-C~ olefins. The calculations described below were performed using data obtained by the Benson method. The next problem under investigation was the influence of the nonideality description on the final equilibrium composition. Colombo et al. (1983)studied the reaction of isobutene with methanol t o MTBE in the liquid phase. They concluded that the experimental values of chemical equilibrium constants of this reaction can be predicted with good accuracy using the standard Gibbs free energy of formation available in literature for the chemicals involved and the UNIFAC estimates of activity coefficients to describe the liquid-phase nonideality. According to this, the UNIFAC method (modified by Larsen et al., 1987) was also used to describe the nonideality of the system considered. However, to determine the influence of the method of the nonideality description on the final equilibrium composition, the calculations were also performed using the ASOG method. Since this method, contrary to the UNIFAC method, is not adapted to systems containing cycloolefins, the calculations were carried out replacing c6 cycloolefins contained in the feed by cyclohexane and C7 cycloolefins by methylcyclohexane for both methods. This operation involved the elimination of the corresponding cycloethers from the model and an increase of the amount of cyclohexane and methylcyclohexane in the feed. The calculated equilibrium compositions as well as the activity coefficients of the individual compounds are presented in Table SIV. It can clearly be seen that both methods of the nonideality description provide very similar results. The calculations described below were performed for the modified UNIFAC method. Table 4 presents the influence of temperature on the calculated equilibrium composition pointing out that the
equilibrium conversion of every kind of the reactive olefins decreases with increasing temperature. This table contains also the experimental results of the pilot plant reported by Pescarollo et al. (1993).The precise quantitative comparison of the calculated and the experimental results cannot be performed, because the detailed experimental feed composition and temperature of the process were not specified. However, confrontation of the results points out that the model was prepared on the basis of reasonable assumptions. It seems also that at pilot plant operating conditions the system does not reach fully the chemical equilibrium state. The program applied facilitates also the calculation of simultaneous chemical and phase equilibria. Table 5 presents the results of the calculations obtained at T = 385 K and at three values of pressures (7.66,5.85, and 4.51bar). At P = 7.66bar the equilibrium product is only a liquid-phase very close to its boiling point. Lowering the pressure about 0.01 bar shifts the system to a simultaneous chemical and phase equilibrium. At 5.85 bar the equilibrium fractions of both phases are nearly the same. At 4.51 bar the system forms only a gas phase. The results presented in Table 5 show a very significant effect of the character of phases the system consists of, on the equilibrium conversion of c4-C~ reactive olefins. A phase reversion (from liquid to gas at constant temperature) is accompanied by a very significant decrease of equilibrium conversions. The effect of phase reversion is more significant than that of temperature. The reason for such a behavior can be found in the numerical values of saturated vapor pressures affecting the chemical potentials of the species in the liquid phase by the second expression of eq 5. The saturated vapor pressures of the reactants (methanol and olefins) are considerably larger than those of the products (ethers). According to this, the Gibbs free energies of the individual etherification reactions in the liquid-phase are more negative than in the gas-phase at the same temperature. Therefore, the tendency of olefins to react t o ethers is much greater in the liquid phase than in the gas phase. The initial estimate used for the calculations of the one-phase system was nearly the same as the feed
1324 Ind. Eng. Chem. Res., Vol. 34,No. 4, 1995 Table 5. Equilibrium Compositions Calculated for Three Different Pressures, at Which the Equilibrium Product Was the Liquid Phase, a Mixture of the Liquid and the Gas Phases, and the Gas Phase, Respectivelp
compound
7.66 liquid phase
methanol isobutene MTBE 2-methyl-2-butene 2-methyl-1-butene 2-methyl-2-methoxybutane 2-methyl-1-pentene 2-methyl-2-pentene 2-methyl-2-methoxypentane cis-3-methyl-2-pentene truns-3-methyl-2-pentene 2-ethyl-1-butene 3-methyl-3-methoxypentane 2,3-dimethyl-l-butene 2,3-dimethyl-2-butene 2,3-dimethyl-2-methoxybutane 1-methylcyclopentene 1-methyl-1-methoxycyclopentane 2-methyl-1-hexene 2-methyl-2-hexene 2-methyl-2-methoxyhexane cis-3-methyl-2-hexene truns-3-methyl-2-hexene cis-3-methyl-3-hexene truns-3-methyl-3-hexene 2-ethyl-1-pentene 3-methyl-3-methoxyhexane 2,3-dimethyl-l-pentene 2,3-dimethyl-2-pentene 2,3-dimethyl-2-methoxypentane cis-3,4-dimethyl-2-pentene truns-3,4-dimethyl-2-pentene 2-ethyl-3-methyl-1-butene 2,3-dimethyl-3-methoxypentane 2,4-dimethyl-l-pentene 2,4-dimethyl-2-pentene 2,4-dimethyl-2-methoxypentane 3-ethyl-2-pentene 3-ethyl-3-methoxypentane 2,3,3-trimethyl-l-butene 2,3,3-trimethyl-2-methoxybutane 1-ethylcyclopentene 1-ethyl-1-methoxycyclopentane 1,2-dimethylcyclopentene l,F~-dimethylcyclopentene 1,2-dimethyl-l-methoxycyclopentane 1,3-dimethylcyclopentene 1,4-dimethylcyclopentene 1,3-dimethyl-l-methoxycyclopentane 1-methylcyclohexene 1-methyl-1-methoxycyclohexane n-butane 1-butene n-pentane 2-methylbutane 1-pentene 3-methyl-1-butene cyclopentane n-hexane 2,2-dimethylbutane 1-hexene 3,3-dimethyl-l-butene cyclohexane benzene n-heptane 2,2,34rimethylbutane 1-heptene methylcyclohexane total
. 11.106
0.014 0.796 2.325 0.329 9.226 0.039 0.282 3.019 0.689 1.467 0.075 2.509 0.017 0.062 0.611 0.246 0.724 0.006 0.058 0.385 0.161 0.152 0.056 0.197 0.009 0.714 0.028 0.466 0.186 0.205 0.218 0.012 0.105 0.035 0.110 0.265 0.216 0.014 0.000 0.010 0.018 0.062 0.042 0.003 0.115 0.003 0.004 0.143 0.000 0.010 0.690 0.670 10.560 10.560 7.320 2.980 1.140 7.910 7.910 6.000 2.380 0.960 3.080 3.600 3.600 3.790 0.410 11 1.106 ~~~
~~
~
gas phase 14.268 0.044 0.349
2.708 0.442 1.915 0.039 0.252 0.509 0.401 0.805 0.047 0.280 0.019 0.047 0.102 0.155 0.067 0.003 0.028 0.037 0.055 0.055
0.020 0.074 0.003 0.051 0.011 0.129 0.011 0.064 0.064 0.004 0.006 0.018 0.055 0.020 0.054 0.001 0.000 0.001 0.006 0.004 0.014 0.001 0.007 0.002 0.003 0.011 0.000 0.001 0.508 0.506 5.965 6.384 4.331 1.907 0.558 3.038 3.809 2.445 1.230 0.301 1.062 0.839 1.127 0.949 0.090 58.309
wt%
isobutene C5 reactive olefins c6 reactive olefins
CTreactive olefins
inert hydrocarbons MTBE Ca ethers C7 ethers CSethers total
0.010 2.321 3.013 ~~. 2.448 73.914 0.875 11.754 9.926 3.254 107.515 4.438 98.3 77.7 ~
methanol isobutene convers,% C5 reactive olefins convers,% c6 reactive olefins convers,% 70.5 C7 reactive olefins convers,% 50.1 a T = 385 K,the feed composition is the same as that in Table SIII.
Pressure,bar 5.85 liquid phase 2.310 0.014 0.403 2.185 0.309 4.319 0.055 0.392 2.093 0.635 1.352 0.069 1.152 0.023 0.084 0.415 0.304 0.445 0.010 0.087 0.286 0.179 0.169 0.062 0.219 0.010 0.394 0.025 0.420 0.083 0.170 0.180 0.010 0.043 0.040 0.126 0.151 0.170 0.006 0.000 0.009 0.025 0.045 0.056 0.004 0.078 0.005 0.007 0.122 0.001 0.009 0.182 0.164 4.595 4.176 2.989 1.073 0.582 4.872 4.101 3.555 1.150 0.659 2.018 2.761 2.473 2.841 0.320 58.269
total 16.576 0.nFiA
0.752 4.893 0.751 6.234 0.094 0.644 2.602 1.036 2.157 0.116 1.432 0.042 0.131 0.517 0.459 0.512 0.013 0.115 0.323 0.234 0.224 0.082 0.293 0.013 0.445 0.036 0.549 0.094 0.234 0.244 0.014 0.049 0.058 0.181 0.171 0.224 0.007 0.000 0.010 0.031 0.049 0.070 0.005 0.085 0.007 0.010 0.133 0.001 0.010 0.690 0.670 10.560 10.560 7.320 2.980 1.140 7.910 7.910 6.000 2.380 0.960 3.080 3.600 3.600 3.790 0.410 116.578
4.51 gas phase 22.829 0.142 0.668 7.524 1.230 3.126 0.222 1.426 1.692 1.340 2.692 0.158 0.550
0.104 0.258 0.328 0.774 0.196 0.029 0.237 0.184 0.299 0.298 0.109 0.403 0.018 0.163 0.050 0.600 0.030 0.255 0.256 0.015 0.013 0.087 0.267 0.056 0.228 0.002 0.000 0.010 0.060 0.020 0.115 0.010 0.035 0.026 0.035 0.090 0.002 0.008 0.690 0.670 10.560 10.560 7.320 2.980 1.140 7.910 7.910 6.000 2.380 0.960 3.080 3.600 3.600 3.790 0.410 122.829
wt%
wt%
0.040 4.937 4.897 3.225 73.914 0.827 7.943 7.323 2.223 105.329 6.624 92.9 52.5 52.1 34.3
0.099 7.655 7.299 4.156 73.914 0.734 3.983 4.004 0.987 102.832 9.122 82.6 26.3 28.6 15.4
*
12*0
12.0
10.0
10.0
8.0
8.0
6.0
6.0
Q 4.0
4.0
2.0
2.0
L
0 n
$ 3 v) v)
E
O . O ~ , , , , , , , , ,, v 340.0
366.0
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1325 can be concluded that the calculated equilibrium overall conversions of the individual groups of c5-c6 reactive olefins can be estimated with the accuracy of a few percent. This accuracy is smaller (about 10%) in the case of the group of C7 olefins, but the amount of these compounds in the light FCC gasoline is much smaller than the amount of c5-c6 olefins. The results of the calculations indicate that the equilibrium conversions are high not only for isobutene but also for C5 and c6 olefins. These conversions increase for olefins with decreasing number of carbon atoms in molecule and decrease with increasing process temperature. At pressures affording the coexistence of two phases, the conversions of the reactive olefins decrease and they reach a minimum (especially for C5C7 olefins) when the equilibrium product is entirely in the gas phase.
, , r , T , , , , , # , , # , ,0.,0F 380.0
40d.0
Temperature, K
Figure 1. Range of existence of the two-phase system in the equilibrium product.
composition presented in Table SIII. The one exception was the number of moles of the individual ethers defined as 0.001. In the case of the two-phase system the number of moles of each hydrocarbon and methanol (for both phases) in the initial estimate were twice smaller than the corresponding feed composition values from Table SIII. The calculations were performed using microcomputer IBM PC/486 and the NDP FORTRAN-386 compiler. The number of iterations and the time of calculations for three examples presented in Table 5 were the following: 13 iterations, 16 s; 20 iterations, 80 s; and 9 iterations, 13 s; respectively. The program used can calculate the range of pressures (at a given temperature) for which the equilibrium product consists of two phases. Figure 1presents such range for the feed composition defined in Table SI11 at the temperature range of 340-400 K.
Conclusions The process of etherification of the light FCC gasoline with methanol has many advantages and can become a very important part of the refinery blocks producing high-octane gasolines in the near future. Complex calculations of the equilibrium compositions allowed to estimate the thermodynamic limits of this process which have not been published up to now. The present paper is the first example of such a study. The high complexity of the process requires some assumptions to be established. It was assumed that the reactions of methanol with reactive olefins are the only ones proceeding in the course of the process. Thereby, the reactions of isomerization of any kind of hydrocarbons and the ethers formed were to be neglected. This assumption is reasonable because under experimental conditions (Pescarollo et al., 1993) the amount of hydrocarbons other than the reactive olefins is nearly the same in the feed and in the products of the process. The lack of thermodynamic data (especially of the standard chemical potentials poi)for C7 olefins and c6CS ethers is a decisive barrier hindering a highly accurate calculation of the equilibrium conversions. Two essentially different methods were applied to estimate the influence of evaluation of poi data by the group contribution methods on the calculated equilibrium compositions. On the basis of the obtained results, it
Acknowledgment This study was sponsored by the Polish State Committee for Scientific Research (Grant No. 957/3/91).The author also acknowledges helpful discussions with Prof. Jerzy Kramarz.
Nomenclature A' = modified formula matrix Ao-A4 = constants in eq 6 = number of atoms of element k in species i b = modified element-abundance vector bk = elemental abundance of element k g = Gibbs free energy of the entire mixture M = number of elements N = number of species ni = number of moles of species i n~ = total number of moles including inerts P = total pressure P, = critical pressure pq = saturated vapor pressure of pure component i R = gas constant T = temperature, K TB= boling temperature, K T,= critical temperature vf. = liquid molar volume of pure component i at T Greek Letters
yi = activity coefficient of species i A = absolute deviation, % pi = chemical potential of species i poi = standard chemical potential of species i (referred to the ideal gas state) & = fugacity coefficient of species i 4: = fugacity coefficient of saturated vapor of pure component i (calculated for T and p : )
Supplementary Material Available: Table SI containing the numerical values of the coefficients AoAq, Table SI1 containing examples illuatrating the accuracy of the group contribution methods applied, Table SI11 containing equilibrium compositions calculated for two different group contribution methods used to obtain the poi values of C7 reactive olefins and (26CS ethers, and Table SIV containing equilibrium compositions calculated for two different methods of the
1326 Ind. Eng. Chem. Res., Vol. 34,No. 4, 1995
liquid-phase nonideality description (7 pages). Ordering information is given on any current masthead page.
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@Abstractpublished in Advance ACS Abstracts, March 1, 1995.
